Solve Linear Systems by Substitution
-$$\begin{array} { l }
9 x + 8 y = 62 \
7 x - 5 y = 37
\end{array}$$
A) $\{ ( 6,1 ) \}$
B) $\{ ( 5,2 ) \}$
C) $\{ ( 6,2 ) \}$
D) $\varnothing$

Question

Solve Linear Systems by Substitution
-$$\begin{array} { l } 
9 x + 8 y = 62 \
7 x - 5 y = 37
\end{array}$$
A) $\{ ( 6,1 ) \}$
B) $\{ ( 5,2 ) \}$
C) $\{ ( 6,2 ) \}$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system of equations by substitution, we can solve one of the equations for one variable and then substitute that expression into the other equation. Solving the first equation for $x$, we get:$$9x = 62 - 8y$$$$x = \frac{62 - 8y}{9}$$Substituting this expression for $x$ in the second equation:$$7\left(\frac{62 - 8y}{9}\right) - 5y = 37$$Multiplying both sides by 9 to clear the denominator:$$7(62 - 8y) - 45y = 333$$$$434 - 56y - 45y = 333$$$$-101y = -101$$$$y = 1$$Substituting $y = 1$ back into the expression for $x$:$$x = \frac{62 - 8(1)}{9}$$$$x = \frac{54}{9}$$$$x = 6$$Therefore, the solution is $(x, y) = (6, 1)$.

Solve Linear Systems by Substitution - 9x+8y=627x−5y=37\begin{array} { l } 9 x + 8 y = 62 \\7 x - 5 y = 37\end{array}9x+8y=627x−5y=37​

Solve Linear Systems by Substitution
- $\begin{array} { l } 9 x + 8 y = 62 \\7 x - 5 y = 37\end{array}$